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After the window closes you cannot send a free form message, but the conversation is not dead. Two things reopen it and one message type survives it.
What reopens the window: any new inbound message from that person. A reply, a new DM, a story reply, another comment that triggers a private reply. Each one restarts the 24 hours from their last message, not from your first.
What survives the window: the human agent message type. It exists so a real person can come back to a customer who asked something on Friday night and did not get a proper answer until Monday. It is for genuine follow up on their question, not for a promotion, and Meta treats misuse of it as a policy problem rather than a rate limit.
What does not work: sending a marketing blast to everyone who ever messaged you. The window is per conversation and it is checked at send time, which is why a broadcast to an old audience shows a pile of skipped recipients rather than an error. If you plan to send a broadcast to people who last wrote weeks ago, expect most of the list to be outside the window.
The practical design change is to stop treating the DM as a place you can return to later. Finish the useful part while they are there: answer, ask the one qualifying question, and if you need to reach them next week, collect an email or a phone number inside the conversation with their consent.